I would rather give the money I'm paying now for health insurance to an organization that is actually concerned with maintaining the health of the american public rather than solely making a profit.
Assuming for a second the government actually does care about your health, that doesn't change the fact the government is horribly inefficient at running pretty much everything. Again you'll just be exchanging one set of problems for another. Instead of people waiting because they can't afford it, they will be waiting because service isn't available. Healthcare is a service and like any service if you reduce the price of it, demand will go up.